## 24.2.1 Energy Equation

The enthalpy of the material is computed as the sum of the sensible enthalpy, , and the latent heat, :

 (24.2-1)

where

 (24.2-2)

 and = reference enthalpy = reference temperature = specific heat at constant pressure

The liquid fraction, , can be defined as

 (24.2-3)

Equation  24.2-3 is referred to as the lever rule .

The latent heat content can now be written in terms of the latent heat of the material, :

 (24.2-4)

The latent heat content can vary between zero (for a solid) and (for a liquid).

In the case of multicomponent solidification with species segregation; i.e., solidification or melting with species transport, the solidus and liquidus temperatures are computed instead of specified (Equations  24.2-5 and 24.2-6).

 (24.2-5) (24.2-6)

where is the partition coefficient of solute , which is the ratio of the concentration in solid to that in liquid at the interface, is the mass fraction of solute , and is the slope of the liquidus surface with respect to . It is assumed that the last species material of the mixture is the solvent and that the other species are the solutes.

For solidification/melting problems, the energy equation is written as

 (24.2-7)

 where = enthalpy (see Equation  24.2-1) = density = fluid velocity = source term

The solution for temperature is essentially an iteration between the energy equation (Equation  24.2-7) and the liquid fraction equation (Equation  24.2-3). Directly using Equation  24.2-3 to update the liquid fraction usually results in poor convergence of the energy equation. In FLUENT, the method suggested by Voller and Swaminathan [ 386] is used to update the liquid fraction. For pure metals, where and are equal, a method based on specific heat, given by Voller and Prakash [ 385], is used instead.

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